August 31, 2004

Calculating the Covered Call Return
by John Brasher, CallWriter Publisher

Every option trader loves calculating investment returns; me, too. I spend a lot of time calculating covered call returns in particular. Whether you use some kind of stock option calculator or just pencil and paper, the question is: how do you calculate the covered call return? This article explains how I make the covered call calculation, and shows you another way to go about it.

The Basic Covered Call Calculation

There are two ways to calculate the covered call return - meaning to calculate the trade's flat return (assumes the trader is not assigned) and the if-called return (assumes that assignment occurs). Simply take the net call premium (the time value part of the premium) and divide it by the cost of the stock. No matter how calculated, the formula for computing the flat covered call return is:

Flat Return

=

Net premium received Cost of stock

Now this is where the dispute comes in: which cost? In other words, should we use the total price paid for the shares before receiving the call premium, or the net cost of the shares after deducting the call premium (the net debit)? Which cost is used makes a difference in the returns, though not a huge one.

For at-the-money (ATM) and out-of-the-money (OTM) calls, the net premium will be the total premium received. For in-the-money (ITM) calls, only the time value portion of the premium is used in the calculation.

Let's Check the Numbers

The following example will illustrate the differences between the price paid and net cost methods. For purposes of the illustration, assume we have bought XYZ shares for $20 and written the at-the-money 20 Call for a $1.00 premium and that the stock is called away at the $20 strike:

As we can see instantly, the dollar amount of the profit is the same - $1.00 - no matter which of the two calculations is used. However, calculating the return using the net cost as the denominator increases the return from 5.00% to 5.25%, because the $1.00 net premium is being divided by $19.00 instead of the $20.00 price paid for the stock. Be clear that the difference results from using the smaller net cost as the divisor instead of the actual price paid for the stock, because we will use another example below.

From 5% to 5.25% is not a big difference; only 1/4 of a point. But principle is involved here, so people can get a bit "exercised" over which one is the proper method to use. Some traders clearly prefer one "option" over the other. My editor is invoking the no-pun rule, so I won't slip any more in.

CallWriter firmly believes that the price paid method should be used.

CallWriter's Real Time Lists™ and Position Management Calculator™ both present covered call returns for all purposes based upon the price paid method. In our experience, most covered call websites and most traders who teach covered calls use the price paid method, but we are aware that a few don't. Again, the only difference is that the net cost method shows a larger return, because the return is computed by dividing cost into the net premium, and the net cost will always be a smaller number than price paid.

So why doesn't CallWriter like to show a larger return? Well, we would love to, but not at the expense of what we see as proper logic and fairness. Plus, we think the net cost calculation is double-dipping. These things are hard to explain, and I'm not a mathematician in any event. But in doing math, it is always good to work the numbers a couple of different ways as a check on the calculations. So instead of arguing mathematical principles, let's use a variant of our comparison table to further compare the two methods by measuring the increase in account size:

 

Example #2	Price Paid Method	Net Cost Method
Bought XYZ shares	-$ 20.00	-$ 20.00
Sold $20 Calls	+$   1.00	+$   1.00
Net debit (breakeven point)	-$ 19.00	-$ 19.00
Sale of Stock When Called	+$ 20.00	+$ 20.00
Cash in Account	$21.00	$21.00
Profit   (cash in account - cost)	$21.00 - $20.00 = $ 1.00	$21.00 - $19.00 = $ 2.00 !!

Once the trade is closed, the $20 stock price is back in the account along with the $1.00 premium. The account has now increased from $20 to $21, a gain of $1.00. However, subtracting the $20.00 price paid gives a $1.00 profit, but subtracting the $19.00 net cost produces a $2.00 profit! Obviously, $2.00 is not the proper return, and the problem stems from using the net cost in the return calculations.

One might say that - just as obviously - you only use the net cost in calculating the percentage return, not the increase in account size. But why? Using the price-paid method gives the same result in both cases; each calculation confirms the other. And just as the net cost method gives a false profit in example #2, it gives a false result when used to calculate the percentage of return,

Look at it this way: when paying $20.00 for the stock and receiving $1.00 for the call, the net cost is clearly $19.00, and the profit is $1.00. But wait a minute... it was paying $20 for the stock and getting the $1.00 premium that created the $19.00 basis. By using the 19.00 basis as the cost, the trader is double-dipping. It would be proper to show a $19 basis only if the trader paid that much for it.

A Couple More Considerations

Here's another point: our hypothetical trade above assumed that the stock was called out for a nicely profitable trade. But suppose that the trade had gone the other way and the trader had to buy back the calls and sell the stock to close the trade at a loss. Would the trader ignore the $20.00 paid and base the final calculation of profit/loss on the $19.00 net cost? No way. The following table assumes the stock declined and the trade was closed at a loss:

Example #3	Price Paid Method	Net Cost Method
Bought XYZ shares	-$ 20.00	-$ 20.00
Sold $20 Calls	+$   1.00	+$   1.00
Net debit (breakeven point)	-$ 19.00	-$ 19.00
Buy back calls to close	-$   0.25	-$   0.25
Sale of stock to close	+$ 17.80	+$ 17.80
Cash in Account	$18.55	$18.55
Profit (Loss)   (cash in account - cost)	$20.00 - $18.55 = $ 1.45	$20.00 - $19.55 = $ 0.45 !!

Again, using the increase/decrease in account, the net cost gives a false number. The actual cash in, cash out difference was a loss of $1.45, not counting trading costs for simplicity. Yet using the net cost of $19.00 shows a loss of only $0.45!  If only this were true! If the net cost was the proper cost to use, it should work no matter how the gain or loss is calculated - - the price-paid method does.

Using the net cost method will show larger percentage returns on winning trades, true, but it will also show correspondingly larger percentage losses on losers (and if it does not, there's monkey business with the numbers). How is that an advantage of any kind?

Finally, using the price paid takes the totality of the trade into account. By comparison, the net cost method - while it inflates the return a bit - ignores the entire trade to focus only on the lower net cost number. Put differently, if the net cost is used, there should be no return on it, because the $1.00 of net premium was obtained by spending $20.00.

I know this article won't change the mind of anyone who really believes the net cost method is more accurate, or just wants to show higher returns. And if you want to use the net cost method in your personal trading records, be my guest. But now you understand how our Real Time Lists™ and Position Management Calculator™ are programmed, and why.

For simplicity of presentation, none of the above calculation examples took commissions or other trading costs into account. Commissions obviously affect returns on real trades.

The If-called Return

The above calculations do not show how to calculate the returns on an OTM trade when the stock is called out (the "if-called return"). When an OTM call is written and the stock is called out, the trader not only keeps the premium but also gets to keep the profit on the stock's price advance up to the calls' strike price - know as the stock profit. The stock profit has to be figured into the if-called return, along with the net premium. The formula is the same as the flat return above, except it takes the stock profit into account:

If-called Return

=

Net premium received + stock profit Cost of stock

Here is a table showing how to make the calculations for OTM calls, using the above XYZ example, but assuming that the 22.50 Call was sold instead of the 20 Call and that the stock was $24 at expiration:

It does not matter, of course, that the stock was at $24 (and thus higher than $22.50), since the trader is called out at the $22.50 strike. However, the trader participated in the stock's advance to the $22.50 level, and unlike the stock trader, collected a nice premium when the covered call was written.

Note that the flat returns and if-called returns on ITM and ATM calls will always be the same amount and same percentage. Only with OTM calls does the trader share in part of the stock profit in addition to the premium and get a larger return when called out.

Good luck and good trading!